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In 1977, J.A. Davis et al showed that any finite subset of natural numbers can be permuted such that it does not contain any 3-term A.P. as a sub-sequence. However, this is not true for the set of all natural numbers.

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Peer reviewing is not just an important part of research, but also one of the main characteristics of scientific temper. However, over millions of years, we have evolved into selfish beings, and we attempt to maximize our benefits.

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We introduce a new information-theoretic complexity measure IC∞ for 2-party functions which is a lower-bound on communication complexity, and has the two leading lower-bounds on communication complexity as its natural relaxations: (external) infor

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The max-coloring problem is to compute a legal coloring of the vertices of a graph $G=(V,E)$ with vertex weights $w$ such that $sum^k_{i=1} max_{v \in C_i} w(v_i)$ is minimized, where $C_1, \ldots ,C_k$ are the various color classes.